| Abstract: | A cyclic ordering of the vertices of a k‐uniform hypergraph is called a hamiltonian chain if any k consecutive vertices in the ordering form an edge. For k = 2 this is the same as a hamiltonian cycle. We consider several natural questions about the new notion. The main result is a Dirac‐type theorem that provides a sufficient condition for finding hamiltonian chains in k‐uniform hypergraphs with large (k ? 1)‐minimal degree. If it is more than  than the hypergraph contains a hamiltonian chain. © 1999 Wiley & Sons, Inc. J Graph Theory 30: 205–212, 1999 |
